{
  "id": "1601.00083",
  "version": "v1",
  "published": "2016-01-01T15:09:21.000Z",
  "updated": "2016-01-01T15:09:21.000Z",
  "title": "A Proof of an Open Problem of Yusuke Nishizawa",
  "authors": [
    "Branko Malesevic",
    "Tatjana Lutovac",
    "Bojan Banjac"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "This paper presents a proof of the following conjecture, stated by Nishizawa in [Appl. Math. Comput. 269, (2015), 146--154.]: for $\\displaystyle 0<x<\\pi/2$ the inequality $ \\displaystyle \\frac{\\sin{x}}{x} \\!>\\! \\left(\\frac{2}{\\pi} + \\frac{\\pi\\!-\\!2}{\\pi^{3}}(\\pi^{2}\\!-\\!4x^{2})\\right)^{\\theta(x)}\\! $ holds, where $\\displaystyle \\theta(x) \\! = \\! -\\frac{(48\\!-\\!24\\pi\\!+\\!\\pi^{3})x^{3} }{3(\\pi\\!-\\!2)\\pi^{3}}+\\frac{\\pi^{3}}{24(\\pi\\!-\\!2)}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-01T15:09:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open problem",
      "yusuke nishizawa",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160100083M"
    }
  }
}